Quantifying the measurement uncertainty of results from environmental analytical methods

The Eurachem-CITAC Guide Quantifying Uncertainty in Analytical Measurement was put into practice in a public laboratory devoted to environmental analytical measurements. In doing so due regard was given to the provisions of ISO 17025 and an attempt was made to base the entire estimation of measurement uncertainty on available data from the literature or from previously performed validation studies. Most environmental analytical procedures laid down in national or international standards are the result of cooperative efforts and put into effect as part of a compromise between all parties involved, public and private, that also encompasses environmental standards and statutory limits. Central to many procedures is the focus on the measurement of environmental effects rather than on individual chemical species. In this situation it is particularly important to understand the measurement process well enough to produce a realistic uncertainty statement. Environmental analytical methods will be examined as far as necessary, but reference will also be made to analytical methods in general and to physical measurement methods where appropriate. This paper describes ways and means of quantifying uncertainty for frequently practised methods of environmental analysis. It will be shown that operationally defined measurands are no obstacle to the estimation process as described in the Eurachem/CITAC Guide if it is accepted that the dominating component of uncertainty comes from the actual practice of the method as a reproducibility standard deviation.     

About acceptance and rejection zones as defined in the EURACHEM/CITAC Guide (2007) “Use of uncertainty information in compliance assessment”

Considering measurement uncertainty is mandatory in assessing conformance to legal or compositional limits, and specific guidelines are available issued by ASME, ISO and Eurachem/CITAC. However, differences between ISO and EURACHEM/CITAC wordings could induce some perplexities in the most careful readers. Possible problems arise from considering that, before performing a test, it should be decided whether it is to be a test for conformity or a test for non-conformity. This choice could perhaps require some renaming of acceptance/rejection zones as defined in the EURACHEM/CITAC Guide. A tentative solution is discussed in this contribution.     

Reply to comments on EURACHEM/CITAC guide “Measurement uncertainty arising from sampling”

The Eurachem/CITAC Guide on ‘Measurement uncertainty arising from sampling’ describes a number of methods and approaches that can be used for the estimation of this uncertainty. A recent comment upon this Guide by Wilrich questions the expression of the measurement uncertainty in a form that is relative to the concentration, rather than just as an absolute number (i.e. as relative expanded uncertainty rather than expanded uncertainty), in one of the worked examples. This reply argues that the measurement results from the ‘duplicate’ method cannot reliably distinguish between constant standard deviation and constant relative standard deviation over the range observed in the example and that the most appropriate model must accordingly rely on prior knowledge. Since extensive prior knowledge indicates that the precision of sampling and of chemical analysis both tend to increase as a function of concentration, the body of the Guide recommends expression as a relative standard deviation. It is acknowledged that this assumption should be restated with the results of the worked examples as well as in its current position in the main body of the text, in a future edition of the Guide.     

A new terminology for the approaches to the quantification of the measurement uncertainty

A new terminology for the approaches to the quantification of the measurement uncertainty is presented, with a view to a better understanding of the available methodologies for the estimation of the measurement quality and differences among them. The knowledge of the merits, disadvantages and differences in the estimation process, of the available approaches, is essential for the production of metrologically correct and fit-to-purpose uncertainty estimations. The presented terminology is based on the level of the analytical information used to estimate the measurement uncertainty (e.g., supralaboratory or intralaboratory information), instead of the direction of information flow (“bottom-up” or “top-down”) towards the level of information where the test is performed, avoiding the use of the same designation for significantly different approaches. The proposed terminology is applied to the approaches considered on 19 examples of the quantification of the measurement uncertainty presented at the Eurachem/CITAC CG4 Guide, Eurolab Technical Report 1/2002 and Nordtest Technical Report 537. Additionally, differences of magnitude in the measurement uncertainty estimated by various approaches are discussed.     

Response to “About acceptance and rejection zones”

Desimoni and Brunetti raise some questions about the use of Eurachem/CITAC guide, because the Eurachem/CITAC guide does not discuss an ISO recommendation before performing a test, it should be decided whether it is to be a test for conformity or a test for non-conformity. In response, it is pointed out that although this recommendation is not discussed explicitly, it is of necessity covered by the decision rule that describes how the measurement uncertainty will be taken into consideration with regard to accepting or rejecting a product according to its specification and the result of a measurement. In addition, they propose the introduction of an ‘inconclusive’ zone. We do not think that this is necessary, since the Eurachem/CITAC guide takes the view that action on rejection should be covered by the ‘decision rule’ and this can make equivalent provision for confirmation or interpretation.     

The uncertainty in the calculation of the amount of blocked and reactive lysine in milk products,as determined by the furosine method

The measurement uncertainty in the calculation of the amount of blocked and reactive lysine (as determined by the furosine method) was evaluated according to the procedure described in the Eurachem/CITAC guide. The analytical method involves the chromatographic determination of lysine and furosine after acid hydrolysis. The calculation of blocked and reactive lysine in the initial protein is based on known conversion factors. The estimation of the uncertainty was performed in two steps: (1) determination of the uncertainty in the chromatographic determination of lysine and furosine, and (2) determination of the uncertainty in the calculation of blocked and reactive lysine. The individual contributions to the final uncertainty were identified, quantified, and combined in uncertainty budgets. The largest contribution to the calculation of blocked lysine came from estimating the conversion factor of blocked lysine into furosine during acid hydrolysis. For the calculation of reactive lysine, the main contribution came from the chromatographic determination of lysine. The uncertainty estimates were compared to available validation data (in-house and collaborative standard deviations of reproducibility).     

Effect of the sample matrix on measurement uncertainty in X-ray fluorescence analysis

The estimation of measurement uncertainty, with reference to univariate calibration functions, is discussed in detail in the Eurachem Guide “Quantifying Uncertainty in Analytical Measurement”. The adoption of these recommendations to quantitative X-ray fluorescence analysis (XRF) involves basic problems which are above all due to the strong influence of the sample matrix on the analytical response. In XRF-analysis, the proposed recommendations are consequently applicable only to the matrix corrected response. The application is also restricted with regard to both the matrices and analyte concentrations.In this context the present studies are aimed at the problems to predict measurement uncertainty also with reference to more variable sample compositions. The corresponding investigations are focused on the use of the intensity of the Compton scattered tube line as an internal standard to assess the effect of the individual sample matrix on the analytical response relatively to a reference matrix. Based on this concept the estimation of the measurement uncertainty of an analyte presented in an unknown specimen can be predicted in consideration of the data obtained under defined matrix conditions.     

Validation of the uncertainty evaluation for the determination of metals in solid samples by atomic spectrometry

 Every analytical result should be expressed with some indication of its quality. The uncertainty as defined by Eurachem ("parameter associated with the result of a measurement that characterises the dispersion of the values that could reasonably be attributed to the, . . ., quantity subjected to measurement") is a good tool to accomplish this goal in quantitative analysis. Eurachem has produced a guide to the estimation of the uncertainty attached to an analytical result. Indeed, the estimation of the total uncertainty by using uncertainty propagation laws is components-dependent. The estimation of some of those components is based on subjective criteria. The identification of the uncertainty sources and of their importance, for the same method, can vary from analyst to analyst. It is important to develop tools which will support each choice and approximation. In this work, the comparison of an estimated uncertainty with an experimentally assessed one, through a variance test, is performed. This approach is applied to the determination by atomic absorption of manganese in digested samples of lettuce leaves. The total uncertainty estimation is calculated assuming 100% digestion efficiency with negligible uncertainty. This assumption was tested. Received: 3 November 1997 · Accepted: 2 January 1998     

Comments to EURACHEM/CITAC guide “Measurement uncertainty arising from sampling”

The EURACHEM/CITAC Guide “Measurement uncertainty arising from sampling” deals with the design and analysis of experiments for the evaluation of the sampling and analytical standard deviation when a defined sampling and analytical method is used for the determination of the concentration, expressed as mass fraction (mg/kg), of an analyte in a specified material. The Guide recommends reporting the relative expanded uncertainty and using it directly, i.e. it implicitly assumes that the standard deviation is proportional to the mass fraction even in case the experimental data do not support this assumption. Example A1 (and some of the other examples of the Guide) demonstrates that this can result in extreme levels of underestimation or overestimation of the uncertainty of measurement results. Hence, such recommendations should be avoided!     

Use of the Eurachem guide on method validation for determination of uranium in environmental samples

Three analytical methods for determination of uranium in environmental samples by a fluorescence technique have been validated and compared in accordance with the Eurachem Guide on method validation. The first method depends on uranium separation from iron using the mercury anode technique; in the other two methods uranium is separated from iron on an anion exchange column by use of either a solution of hydrochloric acid containing ascorbic acid and hydrazine hydrate or a dilute sulfuric acid solution. Detection limits, repeatability, reproducibility, and recovery coefficient were the main validation characteristics. The results showed that better statistical values can be achieved by using the third method. Control charts for in-house control samples and international intercomparison samples have also shown that the third method is more statistically stable with time. In addition, uncertainties of measurement were estimated and compared for the three methods. It was found that the Eurachem Guide and comparison of quality statistical validation data can be good tools for selection of the appropriate method for an application.     

Uncertainty from sampling in measurements of aflatoxins in animal feedingstuffs: application of the Eurachem/CITAC guidelines

The duplicate method for estimating uncertainty from measurement including sampling is presented in the Eurachem/CITAC guide. The applicability of this method as a tool for verifying sampling plans for mycotoxins was assessed in three case studies with aflatoxin B(1) in animal feedingstuffs. Aspects considered included strategies for obtaining samples from contaminated lots, assumptions about distributions, approaches for statistical analysis, log(10)-transformation of test data and applicability of uncertainty estimates. The results showed that when duplicate aggregate samples are formed by interpenetrating sampling, repeated measurements from a lot can be assumed to approximately follow a normal or lognormal distribution. Due to the large variation in toxin concentration between sampling targets and sometimes very large uncertainty arising from sampling and sample preparation (U(rel) ≥ 50%), estimation of uncertainty from log(10)-transformed data was found to be a more generally applicable approach than application of robust ANOVA.     

Measurement uncertainty in the pH measurement procedure

A measured value without even an approximate knowledge of the uncertainty is worthless. The uncertainty is part of every measured value and specification of the uncertainty is part of every analytical procedure. The uncertainty makes the value independent of its origin. The basis for estimation of the uncertainty is the "Guide to the Expression of Uncertainty in Measurement ". For some procedures, however, for example pH measurement, several problems arise in practice. This article describes a practical and inexpensive way of calculating the uncertainty of pH values.     

ICP-MS determination of Pt in biological fluids of patients treated with antitumor agents: evaluation of analytical uncertainty

The estimation of the uncertainty associated to the analytical methods is necessary in order to establish the comparability of results. Methods of Pt determination in biological fluids lack very often of information about uncertainty of results, with likely implications when results are used to interpret the mechanism of action of platinum compound or when they are considered to optimise the clinical therapies.An inductively coupled plasma-mass spectrometer (ICP-MS) method for the determination of Pt in biological fluids (plasma, ultrafiltrate and urine) of patients treated with antitumor agents has been developed and validated. The limits of quantification (LOQ) in the three matrices were 1.0, 0.1, and 2.0 μg/l, respectively.Intraday and interday precisions and accuracies were in good agreement with the FDA criteria for the validation of analytical methods. The validation study was implemented by assessing the uncertainty evaluation for Pt determination in the different matrices according to EURACHEM/CITAC Guide.     

Uncertainty budget for final assay of a pharmaceutical product based on RP–HPLC

Compliance with specified limits for the content of active substance in a pharmaceutical drug requires knowledge of the uncertainty of the final assay. The uncertainty of measurement is based on the ISO recommendation as expressed in the Guide to the Expression of Uncertainty in Measurement (GUM). The reported example illustrates the estimation of uncertainty for the final determination of a protein concentration by HPLC using UV detection, using the approach described by EURACHEM/CITAC. The combined standard uncertainty for a protein concentration of 2400 µmol/L was estimated to be 14 µmol/L.. All known and potential uncertainty components are presented in Ishikawa diagrams and were carefully evaluated using Type A or Type B estimates. Special efforts were made to avoid duplication or omission of significant contributions to the combined uncertainty. Hence, before accepting the uncertainty budget, the estimated combined standard uncertainty was verified using the variation observed in a number of quality control samples.     

Evaluation of measurement uncertainty for analytical procedures using a linear calibration function

In the EURACHEM/CITAC draft ”Quantifying uncertainty in analytical measurement” estimations of measurement uncertainty in analytical results for linear calibration are given. In this work these estimations are compared, i.e. the uncertainty deduced from repeated observations of the sample vs. the uncertainty deduced from the standard residual deviation of the regression. As a result of this study it is shown that an uncertainty estimation based on repeated observations can give more realistic values if the condition of variance homogeneity is not correctly fulfilled in the calibration range. The complete calculation of measurement uncertainty including assessment of trueness is represented by an example concerning the determination of zinc in sediment samples using ICP-atomic emission spectrometry. Received: 9 February 2002 Accepted: 17 April 2002     

Revisiting type-A uncertainties relating to the measurement of mass fraction of lead using isotope-dilution inductively coupled plasma mass spectrometry: a way of improving measurement precision and expanded uncertainty

A quadrupole inductively coupled plasma mass spectrometer (Q-ICP-MS) has been used for determination of lead in plant materials using isotope-dilution inductively coupled plasma mass spectrometry. The accuracy of the method was demonstrated by analysis of a matrix certified reference material, NIST SRM 1547 Peach Leaves. Specific instrumental parameters of Q-ICP-MS, including isotope analysis mode, integration time per point, number of points per mass, and number of measurements, were optimized to obtain the best measurement precision. The precision (expressed as relative standard deviation) associated with replicate measurement of the ²⁰⁸Pb/²⁰⁶Pb isotope ratio and its mass-bias correction factor was <0.2%. Following “Example A7” of the Eurachem/CITAC Guide, the relative expanded uncertainty, U _rel, (coverage factor k = 2) was found to be ±1.1%, which fulfilled the target value of ±2% maximum and was lower than the uncertainty of ±3.4% reported by NIST based on isotope-dilution thermal ionization mass spectrometry. Sample recovery of 99% was obtained.     

Reference materials – a view from a small country

ISO/IEC 17025 has an increased emphasis on traceability and estimation of uncertainty of measurement compared with ISO Guide 25. Demonstration of traceability is a new concept in analytical chemistry and depends on access to relevant reference materials or use of reference methods. Until now most reference materials used in New Zealand have been imported, because they offered international comparability. New Zealand is currently starting to develop the required infrastructure so that it will be able to produce unique reference materials that will contribute to the total international effort in improving the reliability of analytical chemistry. Received: 12 October 2000 / Revised: 18 January 2001 / Accepted: 23 January 2001     

Calibration uncertainty

Methods recommended by the International Standardization Organisation and Eurachem are not satisfactory for the correct estimation of calibration uncertainty. A novel approach is introduced and tested on actual calibration data for the determination of Pb by ICP-AES. The improved calibration uncertainty was verified from independent measurements of the same sample by demonstrating statistical control of analytical results and the absence of bias. The proposed method takes into account uncertainties of the measurement, as well as of the amount of calibrant. It is applicable to all types of calibration data, including cases where linearity can be assumed only over a limited range. Received: 25 August 2001 Accepted: 21 December 2001     

ICP-AES法测定油漆中总铅量不确定度的讨论

根据EURACHEM／CITAC2000中的规定计算了ICP—AES法测定油漆中总铅量的不确定度,建立了数学模型和根据在测试过程中产生不确定度的变量建立了因果图。通过转化数学模型和因果图,对油漆标准样品中含铅量的测定精密度和准确度进行试验,并计算了此方法的不确定度。结论中提出可根据在日常分析试验中所积累的数据,用B类不确定度的计算方法计算所得的测定过程的不确定度具有更高的真实可信性,并指出要不断积累测试数据,不断更新测定方法的不确定度,这样得到的不确定度更为可信合理。     

Uncertainty of measurement and conformity assessment: a review

The uncertainty of measurement is the key indicator of the quality of any experimental result. Proper consideration of this uncertainty is imperative when testing a sample against legal/compositional limits. This task can be quite challenging when the entity measured in the investigated sample is so close to the limit that its uncertainty, however estimated, critically affects decision-making. This explains the many literature contributions discussing the problem. Even though some of the most authoritative organisations have issued specific guidelines aimed at assisting the staff involved in such measurements, several aspects of conformity testing are still debated in the literature. In this review, after a short outline of existing information, somewhat more detailed insight is given into the guidelines of ASME, ISO, and Eurachem/CITAC, because they are the most useful tools for operators of testing and calibration laboratories. Some aspects of Council Directive 96/23/EC are also discussed. Insight into the contents of the mentioned documents enables emphasis of analogies and discrepancies.